I was thinking that if you actually would want this to work better it only needs a small tweek and would only cost you about 5 more dollars at the auto parts store. The only problem you said you have had is slowing the water down to allow it to heat more. One of the problems I see is you are using siphon power which is not all that great, no control over flow rate. The next problem you have is going from one bucket back to the starting bucket, I think that would be a tremendous amount of heat loss not to mention the time spent monitoring the water level.
Try this, you keep the in and out ports of the thermal pane between 4 and 6 inches above the lowest water line, or the inlet. We also do away with the second catch bucket. In fact if you really want to go high tech get yourself one of those insulated water coolers, they will hold heat in just as good as they do the cold. Plus the spout at the bottom will work great for the inlet line. Now make a trip to the autoparts store and tell them you want two one way fuel line valves. The only thing is make sure they have the arrows marked on them so you know which way to install them. They will cost somewhere near 5 dollars for both, unless you tell them you own a Mercedes then you've definitely bumped up the price tag. Next would be to get some line that can hold a little more pressure then a fish tank line. I would suggest about 4 foot of radiator blow-off line, it can hold up to 14 psi and 6 small clamps. The clamps have to be just big enough to get over the line. This will cost approximately another 4 to six dollars for the line and clamps.
Build your thermal collector just as you've done except take your new radiator blow-off line and cut it in half, then take about 3 inches off each line. this will give you 2 - three inch pieces and 2 - 21 inch pieces. Take the three inch pieces and attach them to the inlet and out let ports or tubes of your thermal collector, making sure to put on clamps where the hose and the metal tubes meet, but not too tight don't want to crush the metal tubes and restrict the actual flow capability of the collector. Next you want to install the one way valves, on this part you want one arrow pointing into the collector and the other out or away from the collector. Then after the valves you install the 21 inch lines, you want to make sure you have clamps on both sides of the valves.
At this point you should have your thermal collector and your newly made lines dangling from it. And now for the options, if you went and got a nice thermal jug (igloo), you would connect the inlet line to the water spout at the bottom and lock it open. Open up the breather cap on the top and suck on the return (outlet) line until you get the water past the one way valve that's pointing away from the thermal collector, and put the outlet line through the breather hole in the top of the igloo. Let the sun do its job. Shortly you should have water hot enough to make some tea with, take caution that the water will be extremely hot.
These one way valves have about a 4 pound stopping ability, thus stopping the water in the collector. So even on cloudy days or nominal weather the water would take as long as it needs to heat up. As the water heats up the pressure or psi will increase. When the pressure reaches 4 plus pounds it will expel itself out of the collector and automatically suck in cooler water behind it. Cooler water means less psi and the valves will automatically close to start the whole cycle over again. This will create a continuous cycle of flowing water and again with a word of caution there is no temperature control switch. Since the inlet line will be towards the bottom of the igloo and we already know about convection, the cooler water needing to be heated will be first in line. The only real problem left is to play with the height of the tank in relation to the thermal collector, this is due to the fact that you don't want the water weight to force the water through, and this is dependant on the size of your container. Thus relieving you from having to monitor the water and being on tap whenever you need it. The only extra note is that you will from time to time want to visually check your thermal collector to make sure no leaks have been made from the pressure created during the process.
This setup I think will better suit most folks and for the price of the extra bucket you were using trade it for the valves and blow-off line. I will say though nice work on recycling materials for the thermal collector. Hope to see more in the future.